3 problems

Let $G=(V,E)$ be a graph without isolated edges. An edge $3$-weighting is a map $\omega:E\to\{1,2,3\}$, with weighted degree … at each vertex $v$. The weighting is vertex-colouring…

Harary–Plantholt's conjecture. For every graph $G$,

Czerwiński–Grytczuk–Żelazny's conjecture. For every graph $G$,